Abstract
This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works, we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e., the first order accuracy of the velocities in H 1-norm and the pressure in L 2-norm, as well as the second order accuracy of the velocities in L 2-norm. Besides, we clarify the differences between rectangular and quadrilateral finite element approximation. In addition, we give several examples to verify the validity of our error estimates.
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Huang, Z., Li, Y. A class of nonconforming quadrilateral finite elements for incompressible flow. Sci. China Math. 56, 379–393 (2013). https://doi.org/10.1007/s11425-012-4457-0
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DOI: https://doi.org/10.1007/s11425-012-4457-0